Calculus 2
2
Integration Evaluate the integral 1. ∫ 0 π 4 x 2 sin 2 x dx 2. ∫ 4 (x 2 + 2) 3 2 dx 3. ∫ 3 e 3 x 1 + 9 e 6 x dx 4. ∫ dx √ 6 x − x 2 5. ∫ sin x cos 5 x dx 6. ∫ 1 2 x 3 ln ( 2 x ) dx 7. ∫ dx x √ x 2 + 9 8. ∫ 4 ( x 2 + 1)( x 2 − 1 ) dx 9. ∫ dx √ 3 x 2 − 4 10. ∫ 1 4 x 2 + 8 x + 20 dx 11. ∫ tan 3 x sec 4 x dx 12. ∫ ( ln x ) 2 ⋅ 1 x 2 dx 13. ∫ x 3 + x + 1 x 2 + 2 x + 1 dx 14. ∫ √ 16 − ( x − 2) 2 dx 15. ∫ cot 3 ( 3 x ) cos 2 ( 3 x ) dx 16. ∫ x + 3 x 3 + x dx 17. ∫ √ x 2 − 9 9 x dx 18. ∫ sin ( ln x ) dx 19. ∫ ln 2 ln 3 tanh x sec h 3 x dx
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Exercises on techniques of integration
Transcript of Calculus 2
Integration
Evaluate the integral
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
+
dx
e
9
1
e
3
x
6
x
3
-
2
x
x
6
dx
dx
x
cos
x
sin
5
(
)
2
1
3
dx
x
2
ln
x
+
9
x
x
dx
2
(
)
(
)
-
+
dx
1
x
1
x
4
2
2
-
4
x
3
dx
2
dx
20
x
8
x
4
1
2
+
+
dx
x
sec
x
tan
4
3
(
)
dx
x
1
x
ln
2
2
+
+
+
+
dx
1
x
2
x
1
x
x
2
3
(
)
dx
2
x
16
2
-
-
(
)
(
)
dx
x
3
cos
x
3
cot
2
3
+
+
dx
x
x
3
x
3
dx
x
9
9
x
2
-
(
)
dx
x
ln
sin
3
ln
2
ln
3
dx
x
h
sec
x
tanh
+
3
0
2
1
t
dt
p
4
0
2
dx
x
2
sin
x
(
)
+
dx
2
x
4
2
3
2
